1. Source Search Cointegration Combinations

source("./Mean Reversion/RMR.007 Search Cointegration Combinations.R", echo = FALSE, print.eval = FALSE)
## Parsed with column specification:
## cols(
##   date_unix = col_integer(),
##   date_time = col_datetime(format = ""),
##   high = col_double(),
##   low = col_double(),
##   open = col_double(),
##   close = col_double(),
##   volume = col_double(),
##   quote_volume = col_double(),
##   weighted_average = col_double(),
##   currency_pair = col_character(),
##   period = col_integer()
## )
## [1] "1: Testing for time resolution 900 from 2017-07-07 to 2017-08-23."
## [1] "2: Testing for time resolution 900 from 2017-01-29 to 2017-03-06."
## [1] "3: Testing for time resolution 7200 from 2017-08-10 to 2017-09-27."
## [1] "4: Testing for time resolution 300 from 2017-03-16 to 2017-04-11."
## [1] "5: Testing for time resolution 900 from 2017-06-03 to 2017-06-18."
## [1] "6: Testing for time resolution 900 from 2017-04-17 to 2017-06-01."
## [1] "7: Testing for time resolution 7200 from 2017-08-19 to 2017-10-03."
## [1] "8: Testing for time resolution 14400 from 2017-02-27 to 2017-03-12."
## [1] "9: Testing for time resolution 300 from 2017-05-12 to 2017-06-04."
## [1] "10: Testing for time resolution 86400 from 2017-02-08 to 2017-03-28."
## Parsed with column specification:
## cols(
##   df_stat = col_double(),
##   crit_value_1pct = col_double(),
##   crit_value_5pct = col_double(),
##   crit_value_10pct = col_double(),
##   half_life = col_double(),
##   time_resolution = col_integer(),
##   start_date = col_date(format = ""),
##   end_date = col_date(format = ""),
##   length = col_integer()
## )
## # A tibble: 10 x 14
##    df_stat_mean crit_value_1pct_mean crit_value_5pct_mean
##           <dbl>                <dbl>                <dbl>
##  1    -2.705727                -3.43                -2.86
##  2    -2.205763                -3.43                -2.86
##  3    -2.522380                -3.43                -2.86
##  4    -3.358555                -3.43                -2.86
##  5    -1.919454                -3.43                -2.86
##  6    -2.964059                -3.43                -2.86
##  7    -2.594580                -3.43                -2.86
##  8    -2.211002                -3.51                -2.89
##  9    -3.661327                -3.43                -2.86
## 10    -2.529785                -3.58                -2.93
## # ... with 11 more variables: crit_value_10pct_mean <dbl>,
## #   half_life_mean <dbl>, df_stat_median <dbl>,
## #   crit_value_1pct_median <dbl>, crit_value_5pct_median <dbl>,
## #   crit_value_10pct_median <dbl>, half_life_median <dbl>,
## #   time_resolution <dbl>, start_date <date>, end_date <date>,
## #   length <time>
## Parsed with column specification:
## cols(
##   df_stat_mean = col_double(),
##   crit_value_1pct_mean = col_double(),
##   crit_value_5pct_mean = col_double(),
##   crit_value_10pct_mean = col_double(),
##   half_life_mean = col_double(),
##   df_stat_median = col_double(),
##   crit_value_1pct_median = col_double(),
##   crit_value_5pct_median = col_double(),
##   crit_value_10pct_median = col_double(),
##   half_life_median = col_double(),
##   time_resolution = col_integer(),
##   start_date = col_date(format = ""),
##   end_date = col_date(format = ""),
##   length = col_integer()
## )
## # A tibble: 10 x 14
##    df_stat_mean crit_value_1pct_mean crit_value_5pct_mean
##           <dbl>                <dbl>                <dbl>
##  1    -2.705727                -3.43                -2.86
##  2    -2.205763                -3.43                -2.86
##  3    -2.522380                -3.43                -2.86
##  4    -3.358555                -3.43                -2.86
##  5    -1.919454                -3.43                -2.86
##  6    -2.964059                -3.43                -2.86
##  7    -2.594580                -3.43                -2.86
##  8    -2.211002                -3.51                -2.89
##  9    -3.661327                -3.43                -2.86
## 10    -2.529785                -3.58                -2.93
## # ... with 11 more variables: crit_value_10pct_mean <dbl>,
## #   half_life_mean <dbl>, df_stat_median <dbl>,
## #   crit_value_1pct_median <dbl>, crit_value_5pct_median <dbl>,
## #   crit_value_10pct_median <dbl>, half_life_median <dbl>,
## #   time_resolution <dbl>, start_date <date>, end_date <date>,
## #   length <time>

2. Prepare Data and Calculate Statistics

For each time resolution, prepare the pricing data and test for cointegration for all 98 coin pairs. The date of study is 2017-09-01 to 2017-09-30. This period has exhibited strong mean reversion.

pricing_data_300 <- prepare_data(time_resolution = 300, start_date = "2017-09-01", end_date = "2017-09-30")
pricing_data_900 <- prepare_data(time_resolution = 900, start_date = "2017-09-01", end_date = "2017-09-30")
pricing_data_1800 <- prepare_data(time_resolution = 1800, start_date = "2017-09-01", end_date = "2017-09-30")
pricing_data_7200 <- prepare_data(time_resolution = 7200, start_date = "2017-09-01", end_date = "2017-09-30")
pricing_data_14400 <- prepare_data(time_resolution = 14400, start_date = "2017-09-01", end_date = "2017-09-30")
pricing_data_86400 <- prepare_data(time_resolution = 86400, start_date = "2017-09-01", end_date = "2017-09-30")

coin_pairs_300 <- calculate_statistics(pricing_data = pricing_data_300, coin_pairs = create_coins())
coin_pairs_900 <- calculate_statistics(pricing_data = pricing_data_900, coin_pairs = create_coins())
coin_pairs_1800 <- calculate_statistics(pricing_data = pricing_data_1800, coin_pairs = create_coins())
coin_pairs_7200 <- calculate_statistics(pricing_data = pricing_data_7200, coin_pairs = create_coins())
coin_pairs_14400 <- calculate_statistics(pricing_data = pricing_data_14400, coin_pairs = create_coins())
coin_pairs_86400 <- calculate_statistics(pricing_data = pricing_data_86400, coin_pairs = create_coins())

3. Plot Time Resolution 300

For each time resolution, plot the top 10 coins ranked by the ADF test statistic.

for (i in 1:10) { 
  coin_y <- coin_pairs_300[["coin_y"]][i] 
  coin_x <- coin_pairs_300[["coin_x"]][i] 
  print(str_c("Generating plots for ", coin_y, " and ", coin_x, "."))
  plot_coins(df = pricing_data_300, 
             coin_y = pricing_data_300[[coin_y]], 
             coin_x = pricing_data_300[[coin_x]])
}
## [1] "Generating plots for BTC_XEM and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##          Min           1Q       Median           3Q          Max 
## -0.000007554 -0.000001342  0.000000035  0.000001233  0.000006823 
## 
## Coefficients:
##                 Estimate   Std. Error t value            Pr(>|t|)    
## (Intercept) 0.0000342914 0.0000001786   192.0 <0.0000000000000002 ***
## coin_x      0.0017825242 0.0000119346   149.4 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001836 on 8351 degrees of freedom
## Multiple R-squared:  0.7276, Adjusted R-squared:  0.7276 
## F-statistic: 2.231e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_REP and USDT_BTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8470 -0.5730 -0.1290  0.4191  4.2581 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) -9.76564090  0.10152549  -96.19 <0.0000000000000002 ***
## coin_x       0.00741490  0.00002486  298.23 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8201 on 8351 degrees of freedom
## Multiple R-squared:  0.9142, Adjusted R-squared:  0.9142 
## F-statistic: 8.894e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_BTC and USDT_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -535.99  -52.48   12.85   73.27  231.70 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 1553.1077     8.5097   182.5 <0.0000000000000002 ***
## coin_x       123.2873     0.4134   298.2 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 105.7 on 8351 degrees of freedom
## Multiple R-squared:  0.9142, Adjusted R-squared:  0.9142 
## F-statistic: 8.894e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XMR and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.7857  -1.6548  -0.3121   1.0235  24.4679 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.96177    0.23045   156.1 <0.0000000000000002 ***
## coin_x       1.13133    0.00371   304.9 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.976 on 8351 degrees of freedom
## Multiple R-squared:  0.9176, Adjusted R-squared:  0.9176 
## F-statistic: 9.297e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_LTC and USDT_XMR."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.4296  -1.3426  -0.0774   1.4087  10.5354 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -24.14007    0.28163  -85.72 <0.0000000000000002 ***
## coin_x        0.81106    0.00266  304.91 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.366 on 8351 degrees of freedom
## Multiple R-squared:  0.9176, Adjusted R-squared:  0.9176 
## F-statistic: 9.297e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_REP and USDT_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0293 -0.5929 -0.1819  0.3923  4.1597 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  1.55925    0.07238   21.54 <0.0000000000000002 ***
## coin_x      75.85317    0.28868  262.76 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9195 on 8351 degrees of freedom
## Multiple R-squared:  0.8921, Adjusted R-squared:  0.8921 
## F-statistic: 6.904e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XEM and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.036125 -0.007592  0.002155  0.006693  0.040358 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) 0.074905407 0.000590279   126.9 <0.0000000000000002 ***
## coin_x      0.002842819 0.000009504   299.1 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01018 on 8351 degrees of freedom
## Multiple R-squared:  0.9146, Adjusted R-squared:  0.9146 
## F-statistic: 8.947e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XEM and USDT_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.050135 -0.004313  0.001641  0.007033  0.030006 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.00845403 0.00092134   9.176 <0.0000000000000002 ***
## coin_x      0.01176083 0.00004476 262.759 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01145 on 8351 degrees of freedom
## Multiple R-squared:  0.8921, Adjusted R-squared:  0.8921 
## F-statistic: 6.904e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_LTC and BTC_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00261762 -0.00071480 -0.00007712  0.00068928  0.00282866 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept)  -0.0099463   0.0001665  -59.75 <0.0000000000000002 ***
## coin_x      408.1931633   2.7329907  149.36 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0008788 on 8351 degrees of freedom
## Multiple R-squared:  0.7276, Adjusted R-squared:  0.7276 
## F-statistic: 2.231e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_REP and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00046389 -0.00013994 -0.00004017  0.00010558  0.00093721 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.00318938 0.00001868  170.71 <0.0000000000000002 ***
## coin_x      0.12142256 0.00124820   97.28 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0001921 on 8351 degrees of freedom
## Multiple R-squared:  0.5312, Adjusted R-squared:  0.5312 
## F-statistic:  9463 on 1 and 8351 DF,  p-value: < 0.00000000000000022

4. Plot Time Resolution 900

for (i in 1:10) { 
  coin_y <- coin_pairs_900[["coin_y"]][i] 
  coin_x <- coin_pairs_900[["coin_x"]][i] 
  print(str_c("Generating plots for ", coin_y, " and ", coin_x, "."))
  plot_coins(df = pricing_data_900, 
             coin_y = pricing_data_900[[coin_y]], 
             coin_x = pricing_data_900[[coin_x]])
}
## [1] "Generating plots for BTC_XEM and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##          Min           1Q       Median           3Q          Max 
## -0.000007554 -0.000001345  0.000000029  0.000001240  0.000006653 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) 0.000034272 0.000000309  110.92 <0.0000000000000002 ***
## coin_x      0.001783861 0.000020643   86.41 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001835 on 2783 degrees of freedom
## Multiple R-squared:  0.7285, Adjusted R-squared:  0.7284 
## F-statistic:  7467 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XMR and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.7046  -1.6898  -0.3227   1.0009  24.1214 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.967359   0.398511   90.25 <0.0000000000000002 ***
## coin_x       1.131332   0.006417  176.29 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.971 on 2783 degrees of freedom
## Multiple R-squared:  0.9178, Adjusted R-squared:  0.9178 
## F-statistic: 3.108e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_LTC and USDT_XMR."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.1291  -1.3225  -0.0763   1.4338   8.8500 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -24.167337   0.487184  -49.61 <0.0000000000000002 ***
## coin_x        0.811269   0.004602  176.29 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.362 on 2783 degrees of freedom
## Multiple R-squared:  0.9178, Adjusted R-squared:  0.9178 
## F-statistic: 3.108e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_LTC and BTC_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00239641 -0.00071868 -0.00008315  0.00069136  0.00283113 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept)  -0.0099584   0.0002878  -34.60 <0.0000000000000002 ***
## coin_x      408.3809852   4.7259022   86.41 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000878 on 2783 degrees of freedom
## Multiple R-squared:  0.7285, Adjusted R-squared:  0.7284 
## F-statistic:  7467 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XEM and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.036125 -0.007577  0.002205  0.006700  0.039886 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.07487695 0.00102019   73.39 <0.0000000000000002 ***
## coin_x      0.00284344 0.00001643  173.08 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01017 on 2783 degrees of freedom
## Multiple R-squared:  0.915,  Adjusted R-squared:  0.915 
## F-statistic: 2.996e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_REP and USDT_BTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7288 -0.5774 -0.1290  0.4189  4.2573 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) -9.73062649  0.17668477  -55.07 <0.0000000000000002 ***
## coin_x       0.00740622  0.00004327  171.16 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8245 on 2783 degrees of freedom
## Multiple R-squared:  0.9132, Adjusted R-squared:  0.9132 
## F-statistic: 2.929e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_BTC and USDT_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -536.07  -53.24   12.89   73.00  215.86 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 1552.7191    14.8285   104.7 <0.0000000000000002 ***
## coin_x       123.3072     0.7204   171.2 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 106.4 on 2783 degrees of freedom
## Multiple R-squared:  0.9132, Adjusted R-squared:  0.9132 
## F-statistic: 2.929e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_REP and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00046354 -0.00013934 -0.00004032  0.00010333  0.00093508 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.00318550 0.00003238   98.39 <0.0000000000000002 ***
## coin_x      0.12167755 0.00216326   56.25 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0001923 on 2783 degrees of freedom
## Multiple R-squared:  0.532,  Adjusted R-squared:  0.5318 
## F-statistic:  3164 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_LTC and USDT_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.6060  -2.7107  -0.7245   2.8581  10.3138 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -18.9112     0.4661  -40.57 <0.0000000000000002 ***
## coin_x      321.7923     1.8592  173.08 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.42 on 2783 degrees of freedom
## Multiple R-squared:  0.915,  Adjusted R-squared:  0.915 
## F-statistic: 2.996e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_REP and USDT_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9671 -0.5868 -0.1877  0.3978  4.0641 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)   1.5685     0.1255    12.5 <0.0000000000000002 ***
## coin_x       75.8143     0.5005   151.5 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9206 on 2783 degrees of freedom
## Multiple R-squared:  0.8918, Adjusted R-squared:  0.8918 
## F-statistic: 2.294e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

5. Plot Time Resolution 1800

for (i in 1:10) { 
  coin_y <- coin_pairs_1800[["coin_y"]][i] 
  coin_x <- coin_pairs_1800[["coin_x"]][i] 
  print(str_c("Generating plots for ", coin_y, " and ", coin_x, "."))
  plot_coins(df = pricing_data_1800, 
             coin_y = pricing_data_1800[[coin_y]], 
             coin_x = pricing_data_1800[[coin_x]])
}
## [1] "Generating plots for USDT_XMR and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.6872  -1.6639  -0.3182   0.9912  24.1493 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.992859   0.560945   64.17 <0.0000000000000002 ***
## coin_x       1.130652   0.009035  125.14 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.957 on 1391 degrees of freedom
## Multiple R-squared:  0.9184, Adjusted R-squared:  0.9184 
## F-statistic: 1.566e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_LTC and USDT_XMR."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.1857  -1.3133  -0.0869   1.3680   8.8470 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -24.263151   0.686976  -35.32 <0.0000000000000002 ***
## coin_x        0.812293   0.006491  125.14 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.354 on 1391 degrees of freedom
## Multiple R-squared:  0.9184, Adjusted R-squared:  0.9184 
## F-statistic: 1.566e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_XEM and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##           Min            1Q        Median            3Q           Max 
## -0.0000075557 -0.0000013567 -0.0000000041  0.0000012434  0.0000065578 
## 
## Coefficients:
##                 Estimate   Std. Error t value            Pr(>|t|)    
## (Intercept) 0.0000343156 0.0000004359   78.73 <0.0000000000000002 ***
## coin_x      0.0017808785 0.0000291278   61.14 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001833 on 1391 degrees of freedom
## Multiple R-squared:  0.7288, Adjusted R-squared:  0.7286 
## F-statistic:  3738 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_REP and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00046434 -0.00013920 -0.00003941  0.00010537  0.00093452 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.00318808 0.00004553   70.02 <0.0000000000000002 ***
## coin_x      0.12154940 0.00304290   39.95 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0001915 on 1391 degrees of freedom
## Multiple R-squared:  0.5343, Adjusted R-squared:  0.5339 
## F-statistic:  1596 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_REP and USDT_BTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7184 -0.5726 -0.1294  0.4224  4.2610 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) -9.76197830  0.24983070  -39.07 <0.0000000000000002 ***
## coin_x       0.00741325  0.00006119  121.15 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8245 on 1391 degrees of freedom
## Multiple R-squared:  0.9134, Adjusted R-squared:  0.9134 
## F-statistic: 1.468e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_BTC and USDT_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -536.07  -52.98   12.34   72.77  213.84 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 1554.891     20.929    74.3 <0.0000000000000002 ***
## coin_x       123.216      1.017   121.1 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 106.3 on 1391 degrees of freedom
## Multiple R-squared:  0.9134, Adjusted R-squared:  0.9134 
## F-statistic: 1.468e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_LTC and BTC_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00240240 -0.00071702 -0.00008127  0.00069541  0.00283937 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept)  -0.0100109   0.0004076  -24.56 <0.0000000000000002 ***
## coin_x      409.2378593   6.6934448   61.14 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0008786 on 1391 degrees of freedom
## Multiple R-squared:  0.7288, Adjusted R-squared:  0.7286 
## F-statistic:  3738 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XEM and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.036170 -0.007597  0.002155  0.006782  0.039936 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.07506118 0.00143767   52.21 <0.0000000000000002 ***
## coin_x      0.00284034 0.00002316  122.66 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01014 on 1391 degrees of freedom
## Multiple R-squared:  0.9154, Adjusted R-squared:  0.9153 
## F-statistic: 1.504e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_REP and USDT_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9281 -0.6116 -0.1834  0.3915  4.0667 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)   1.5433     0.1779   8.677 <0.0000000000000002 ***
## coin_x       75.9092     0.7095 106.983 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9225 on 1391 degrees of freedom
## Multiple R-squared:  0.8916, Adjusted R-squared:  0.8916 
## F-statistic: 1.145e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XEM and USDT_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.048842 -0.004445  0.001537  0.007044  0.028590 
## 
## Coefficients:
##              Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 0.0087709  0.0022593   3.882             0.000108 ***
## coin_x      0.0117461  0.0001098 106.983 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01148 on 1391 degrees of freedom
## Multiple R-squared:  0.8916, Adjusted R-squared:  0.8916 
## F-statistic: 1.145e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

6. Plot Time Resolution 7200

for (i in 1:10) { 
  coin_y <- coin_pairs_7200[["coin_y"]][i] 
  coin_x <- coin_pairs_7200[["coin_x"]][i] 
  print(str_c("Generating plots for ", coin_y, " and ", coin_x, "."))
  plot_coins(df = pricing_data_7200, 
             coin_y = pricing_data_7200[[coin_y]], 
             coin_x = pricing_data_7200[[coin_x]])
}
## [1] "Generating plots for USDT_XMR and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.6386  -1.6524  -0.2642   0.9648  19.3184 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.99738    1.08940   33.04 <0.0000000000000002 ***
## coin_x       1.12981    0.01756   64.34 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.855 on 347 degrees of freedom
## Multiple R-squared:  0.9227, Adjusted R-squared:  0.9224 
## F-statistic:  4140 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_XEM and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##           Min            1Q        Median            3Q           Max 
## -0.0000075117 -0.0000013231 -0.0000000155  0.0000012043  0.0000060980 
## 
## Coefficients:
##                 Estimate   Std. Error t value            Pr(>|t|)    
## (Intercept) 0.0000341619 0.0000008857   38.57 <0.0000000000000002 ***
## coin_x      0.0017887492 0.0000592241   30.20 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001867 on 347 degrees of freedom
## Multiple R-squared:  0.7244, Adjusted R-squared:  0.7236 
## F-statistic: 912.2 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_LTC and USDT_XMR."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.3973  -1.2895   0.0341   1.3039   8.8491 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -24.68618    1.34197  -18.39 <0.0000000000000002 ***
## coin_x        0.81665    0.01269   64.34 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.278 on 347 degrees of freedom
## Multiple R-squared:  0.9227, Adjusted R-squared:  0.9224 
## F-statistic:  4140 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_ETH and BTC_DASH."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0038536 -0.0016410 -0.0004824  0.0009370  0.0104390 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 0.057670   0.001762   32.72 < 0.0000000000000002 ***
## coin_x      0.182259   0.021670    8.41  0.00000000000000108 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002588 on 347 degrees of freedom
## Multiple R-squared:  0.1693, Adjusted R-squared:  0.1669 
## F-statistic: 70.74 on 1 and 347 DF,  p-value: 0.000000000000001076

## [1] "Generating plots for USDT_REP and USDT_BTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5779 -0.6011 -0.1128  0.4236  2.6516 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -9.7521113  0.4882912  -19.97 <0.0000000000000002 ***
## coin_x       0.0074100  0.0001196   61.95 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8108 on 347 degrees of freedom
## Multiple R-squared:  0.9171, Adjusted R-squared:  0.9168 
## F-statistic:  3838 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XEM and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.035870 -0.007766  0.002150  0.007063  0.035942 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.07418121 0.00289484   25.62 <0.0000000000000002 ***
## coin_x      0.00285327 0.00004666   61.15 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01024 on 347 degrees of freedom
## Multiple R-squared:  0.9151, Adjusted R-squared:  0.9148 
## F-statistic:  3739 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_REP and BTC_DASH."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00062429 -0.00015017 -0.00003047  0.00010655  0.00088295 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  0.0068374  0.0001621   42.19 <0.0000000000000002 ***
## coin_x      -0.0227435  0.0019925  -11.41 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0002379 on 347 degrees of freedom
## Multiple R-squared:  0.273,  Adjusted R-squared:  0.2709 
## F-statistic: 130.3 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_BTC and USDT_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -341.11  -55.55   11.93   74.44  200.80 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 1544.101     41.095   37.57 <0.0000000000000002 ***
## coin_x       123.762      1.998   61.95 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 104.8 on 347 degrees of freedom
## Multiple R-squared:  0.9171, Adjusted R-squared:  0.9168 
## F-statistic:  3838 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_REP and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00043187 -0.00013841 -0.00003465  0.00010510  0.00059920 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.00319881 0.00009016   35.48 <0.0000000000000002 ***
## coin_x      0.12076320 0.00602842   20.03 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.00019 on 347 degrees of freedom
## Multiple R-squared:  0.5363, Adjusted R-squared:  0.5349 
## F-statistic: 401.3 on 1 and 347 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_LTC and BTC_XEM."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00211385 -0.00073957 -0.00009388  0.00070228  0.00278791 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept)  -0.0097405   0.0008159  -11.94 <0.0000000000000002 ***
## coin_x      404.9946207  13.4090534   30.20 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0008883 on 347 degrees of freedom
## Multiple R-squared:  0.7244, Adjusted R-squared:  0.7236 
## F-statistic: 912.2 on 1 and 347 DF,  p-value: < 0.00000000000000022

7. Plot Time Resolution 14400

for (i in 1:10) { 
  coin_y <- coin_pairs_14400[["coin_y"]][i] 
  coin_x <- coin_pairs_14400[["coin_x"]][i] 
  print(str_c("Generating plots for ", coin_y, " and ", coin_x, "."))
  plot_coins(df = pricing_data_14400, 
             coin_y = pricing_data_14400[[coin_y]], 
             coin_x = pricing_data_14400[[coin_x]])
}
## [1] "Generating plots for USDT_XMR and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.5723  -1.8244  -0.2084   0.9656  19.3276 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.71162    1.51967   23.50 <0.0000000000000002 ***
## coin_x       1.13329    0.02451   46.24 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.818 on 173 degrees of freedom
## Multiple R-squared:  0.9251, Adjusted R-squared:  0.9247 
## F-statistic:  2138 on 1 and 173 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_LTC and USDT_XMR."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.4427  -1.3155   0.0483   1.2022   8.7895 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -24.59567    1.86460  -13.19 <0.0000000000000002 ***
## coin_x        0.81633    0.01765   46.24 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.241 on 173 degrees of freedom
## Multiple R-squared:  0.9251, Adjusted R-squared:  0.9247 
## F-statistic:  2138 on 1 and 173 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_ETH and BTC_DASH."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0038341 -0.0016368 -0.0004610  0.0009655  0.0099446 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 0.057726   0.002486   23.22 < 0.0000000000000002 ***
## coin_x      0.181335   0.030577    5.93          0.000000016 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002568 on 173 degrees of freedom
## Multiple R-squared:  0.1689, Adjusted R-squared:  0.1641 
## F-statistic: 35.17 on 1 and 173 DF,  p-value: 0.00000001602

## [1] "Generating plots for BTC_XEM and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##           Min            1Q        Median            3Q           Max 
## -0.0000074526 -0.0000012903  0.0000000175  0.0000011949  0.0000057830 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) 0.000033667 0.000001276   26.39 <0.0000000000000002 ***
## coin_x      0.001819995 0.000085378   21.32 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001909 on 173 degrees of freedom
## Multiple R-squared:  0.7243, Adjusted R-squared:  0.7227 
## F-statistic: 454.4 on 1 and 173 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_XEM and USDT_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.035518 -0.006721  0.001962  0.007202  0.031888 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.07280959 0.00410622   17.73 <0.0000000000000002 ***
## coin_x      0.00287598 0.00006622   43.43 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01032 on 173 degrees of freedom
## Multiple R-squared:  0.916,  Adjusted R-squared:  0.9155 
## F-statistic:  1886 on 1 and 173 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_REP and BTC_DASH."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00061706 -0.00014454 -0.00002468  0.00009220  0.00081652 
## 
## Coefficients:
##               Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)  0.0067990  0.0002285   29.75 < 0.0000000000000002 ***
## coin_x      -0.0223197  0.0028111   -7.94    0.000000000000245 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0002361 on 173 degrees of freedom
## Multiple R-squared:  0.2671, Adjusted R-squared:  0.2628 
## F-statistic: 63.04 on 1 and 173 DF,  p-value: 0.0000000000002455

## [1] "Generating plots for BTC_REP and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00043173 -0.00013070 -0.00002933  0.00010251  0.00056316 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.0032174  0.0001248   25.77 <0.0000000000000002 ***
## coin_x      0.1194186  0.0083552   14.29 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0001868 on 173 degrees of freedom
## Multiple R-squared:  0.5415, Adjusted R-squared:  0.5388 
## F-statistic: 204.3 on 1 and 173 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_ETH and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0047124 -0.0021563 -0.0002285  0.0013427  0.0098794 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.070450   0.001877  37.531 <0.0000000000000002 ***
## coin_x      0.132759   0.125633   1.057               0.292    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002808 on 173 degrees of freedom
## Multiple R-squared:  0.006413,   Adjusted R-squared:  0.00067 
## F-statistic: 1.117 on 1 and 173 DF,  p-value: 0.2921

## [1] "Generating plots for BTC_ETH and BTC_XMR."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0049713 -0.0021473 -0.0000822  0.0013244  0.0097292 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.069648   0.003246  21.459 <0.0000000000000002 ***
## coin_x      0.107997   0.126095   0.856               0.393    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002811 on 173 degrees of freedom
## Multiple R-squared:  0.004222,   Adjusted R-squared:  -0.001534 
## F-statistic: 0.7335 on 1 and 173 DF,  p-value: 0.3929

## [1] "Generating plots for BTC_ETH and BTC_ZEC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0043253 -0.0019186 -0.0003149  0.0012466  0.0094418 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 0.066200   0.001445  45.810 < 0.0000000000000002 ***
## coin_x      0.113922   0.026202   4.348            0.0000234 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002675 on 173 degrees of freedom
## Multiple R-squared:  0.09851,    Adjusted R-squared:  0.09329 
## F-statistic:  18.9 on 1 and 173 DF,  p-value: 0.00002342

8. Plot Time Resolution 86400

for (i in 1:10) { 
  coin_y <- coin_pairs_86400[["coin_y"]][i] 
  coin_x <- coin_pairs_86400[["coin_x"]][i] 
  print(str_c("Generating plots for ", coin_y, " and ", coin_x, "."))
  plot_coins(df = pricing_data_86400, 
             coin_y = pricing_data_86400[[coin_y]], 
             coin_x = pricing_data_86400[[coin_x]])
}
## [1] "Generating plots for BTC_ETH and BTC_DASH."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.003306 -0.001553 -0.000233  0.001127  0.004917 
## 
## Coefficients:
##             Estimate Std. Error t value         Pr(>|t|)    
## (Intercept) 0.058642   0.005179  11.323 0.00000000000927 ***
## coin_x      0.167030   0.063661   2.624           0.0141 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002105 on 27 degrees of freedom
## Multiple R-squared:  0.2032, Adjusted R-squared:  0.1737 
## F-statistic: 6.884 on 1 and 27 DF,  p-value: 0.01413

## [1] "Generating plots for BTC_REP and BTC_DASH."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00028213 -0.00010269  0.00002135  0.00006380  0.00035581 
## 
## Coefficients:
##               Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)  0.0068313  0.0004061  16.824 0.000000000000000776 ***
## coin_x      -0.0229002  0.0049910  -4.588 0.000092072428839062 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0001651 on 27 degrees of freedom
## Multiple R-squared:  0.4381, Adjusted R-squared:  0.4173 
## F-statistic: 21.05 on 1 and 27 DF,  p-value: 0.00009207

## [1] "Generating plots for BTC_ETH and BTC_XMR."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0032331 -0.0018057 -0.0002109  0.0012201  0.0046517 
## 
## Coefficients:
##              Estimate Std. Error t value        Pr(>|t|)    
## (Intercept)  0.075642   0.007091  10.667 0.0000000000349 ***
## coin_x      -0.135217   0.277424  -0.487            0.63    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002348 on 27 degrees of freedom
## Multiple R-squared:  0.008722,   Adjusted R-squared:  -0.02799 
## F-statistic: 0.2376 on 1 and 27 DF,  p-value: 0.6299

## [1] "Generating plots for USDT_BTC and USDT_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -226.243  -45.628    0.156   62.820  208.665 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 1254.135    152.999   8.197         0.0000000084 ***
## coin_x       138.297      7.512  18.409 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 97.35 on 27 degrees of freedom
## Multiple R-squared:  0.9262, Adjusted R-squared:  0.9235 
## F-statistic: 338.9 on 1 and 27 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for USDT_REP and USDT_BTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.4944 -0.3292 -0.1622  0.4061  1.5361 
## 
## Coefficients:
##               Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) -6.9069160  1.4791046   -4.67             0.000074 ***
## coin_x       0.0066972  0.0003638   18.41 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6775 on 27 degrees of freedom
## Multiple R-squared:  0.9262, Adjusted R-squared:  0.9235 
## F-statistic: 338.9 on 1 and 27 DF,  p-value: < 0.00000000000000022

## [1] "Generating plots for BTC_ETH and BTC_ZEC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0033457 -0.0016413 -0.0004947  0.0012814  0.0046917 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.067954   0.003514  19.336 <0.0000000000000002 ***
## coin_x      0.077761   0.064010   1.215               0.235    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002297 on 27 degrees of freedom
## Multiple R-squared:  0.05183,    Adjusted R-squared:  0.01671 
## F-statistic: 1.476 on 1 and 27 DF,  p-value: 0.2349

## [1] "Generating plots for BTC_ETH and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0032889 -0.0018485  0.0000349  0.0011442  0.0048716 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 0.071685   0.003874  18.505 <0.0000000000000002 ***
## coin_x      0.034509   0.261678   0.132               0.896    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002358 on 27 degrees of freedom
## Multiple R-squared:  0.0006437,  Adjusted R-squared:  -0.03637 
## F-statistic: 0.01739 on 1 and 27 DF,  p-value: 0.8961

## [1] "Generating plots for USDT_ETH and USDT_BTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.032  -6.920  -1.184   4.843  20.412 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -18.746489  20.421114  -0.918               0.367    
## coin_x        0.076925   0.005023  15.315 0.00000000000000777 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.354 on 27 degrees of freedom
## Multiple R-squared:  0.8968, Adjusted R-squared:  0.8929 
## F-statistic: 234.6 on 1 and 27 DF,  p-value: 0.00000000000000777

## [1] "Generating plots for BTC_REP and BTC_LTC."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##         Min          1Q      Median          3Q         Max 
## -0.00022344 -0.00010018 -0.00001669  0.00007055  0.00048623 
## 
## Coefficients:
##              Estimate Std. Error t value           Pr(>|t|)    
## (Intercept) 0.0035797  0.0002408  14.863 0.0000000000000161 ***
## coin_x      0.0947604  0.0162691   5.825 0.0000033630484185 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0001466 on 27 degrees of freedom
## Multiple R-squared:  0.5568, Adjusted R-squared:  0.5404 
## F-statistic: 33.93 on 1 and 27 DF,  p-value: 0.000003363

## [1] "Generating plots for BTC_ETH and BTC_REP."
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0031017 -0.0019468 -0.0002738  0.0012263  0.0049217 
## 
## Coefficients:
##             Estimate Std. Error t value    Pr(>|t|)    
## (Intercept)  0.06703    0.01021   6.563 0.000000487 ***
## coin_x       1.03833    2.05160   0.506       0.617    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.002348 on 27 degrees of freedom
## Multiple R-squared:  0.009398,   Adjusted R-squared:  -0.02729 
## F-statistic: 0.2561 on 1 and 27 DF,  p-value: 0.6169

9. BTC_XEM and BTC_LTC Coin Pair

An examination of BTC_XEM and BTC_LTC across time resolutions.

plot_coins(df = pricing_data_300, 
           coin_y = pricing_data_300[["BTC_XEM"]], 
           coin_x = pricing_data_300[["BTC_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##          Min           1Q       Median           3Q          Max 
## -0.000007554 -0.000001342  0.000000035  0.000001233  0.000006823 
## 
## Coefficients:
##                 Estimate   Std. Error t value            Pr(>|t|)    
## (Intercept) 0.0000342914 0.0000001786   192.0 <0.0000000000000002 ***
## coin_x      0.0017825242 0.0000119346   149.4 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001836 on 8351 degrees of freedom
## Multiple R-squared:  0.7276, Adjusted R-squared:  0.7276 
## F-statistic: 2.231e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_900, 
           coin_y = pricing_data_900[["BTC_XEM"]], 
           coin_x = pricing_data_900[["BTC_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##          Min           1Q       Median           3Q          Max 
## -0.000007554 -0.000001345  0.000000029  0.000001240  0.000006653 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) 0.000034272 0.000000309  110.92 <0.0000000000000002 ***
## coin_x      0.001783861 0.000020643   86.41 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001835 on 2783 degrees of freedom
## Multiple R-squared:  0.7285, Adjusted R-squared:  0.7284 
## F-statistic:  7467 on 1 and 2783 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_1800, 
           coin_y = pricing_data_1800[["BTC_XEM"]], 
           coin_x = pricing_data_1800[["BTC_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##           Min            1Q        Median            3Q           Max 
## -0.0000075557 -0.0000013567 -0.0000000041  0.0000012434  0.0000065578 
## 
## Coefficients:
##                 Estimate   Std. Error t value            Pr(>|t|)    
## (Intercept) 0.0000343156 0.0000004359   78.73 <0.0000000000000002 ***
## coin_x      0.0017808785 0.0000291278   61.14 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001833 on 1391 degrees of freedom
## Multiple R-squared:  0.7288, Adjusted R-squared:  0.7286 
## F-statistic:  3738 on 1 and 1391 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_7200, 
           coin_y = pricing_data_7200[["BTC_XEM"]], 
           coin_x = pricing_data_7200[["BTC_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##           Min            1Q        Median            3Q           Max 
## -0.0000075117 -0.0000013231 -0.0000000155  0.0000012043  0.0000060980 
## 
## Coefficients:
##                 Estimate   Std. Error t value            Pr(>|t|)    
## (Intercept) 0.0000341619 0.0000008857   38.57 <0.0000000000000002 ***
## coin_x      0.0017887492 0.0000592241   30.20 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001867 on 347 degrees of freedom
## Multiple R-squared:  0.7244, Adjusted R-squared:  0.7236 
## F-statistic: 912.2 on 1 and 347 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_14400, 
           coin_y = pricing_data_14400[["BTC_XEM"]], 
           coin_x = pricing_data_14400[["BTC_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##           Min            1Q        Median            3Q           Max 
## -0.0000074526 -0.0000012903  0.0000000175  0.0000011949  0.0000057830 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) 0.000033667 0.000001276   26.39 <0.0000000000000002 ***
## coin_x      0.001819995 0.000085378   21.32 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000001909 on 173 degrees of freedom
## Multiple R-squared:  0.7243, Adjusted R-squared:  0.7227 
## F-statistic: 454.4 on 1 and 173 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_86400, 
           coin_y = pricing_data_86400[["BTC_XEM"]], 
           coin_x = pricing_data_86400[["BTC_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##           Min            1Q        Median            3Q           Max 
## -0.0000072622 -0.0000010911  0.0000001578  0.0000013416  0.0000027461 
## 
## Coefficients:
##                Estimate  Std. Error t value       Pr(>|t|)    
## (Intercept) 0.000034025 0.000003437   9.899 0.000000000176 ***
## coin_x      0.001780634 0.000232186   7.669 0.000000030065 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.000002092 on 27 degrees of freedom
## Multiple R-squared:  0.6854, Adjusted R-squared:  0.6737 
## F-statistic: 58.81 on 1 and 27 DF,  p-value: 0.00000003007

9. USDT_REP and USDT_BTC Coin Pair

An examination of USDT_REP and USDT_BTC across time resolutions.

plot_coins(df = pricing_data_300, 
           coin_y = pricing_data_300[["USDT_REP"]], 
           coin_x = pricing_data_300[["USDT_BTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8470 -0.5730 -0.1290  0.4191  4.2581 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) -9.76564090  0.10152549  -96.19 <0.0000000000000002 ***
## coin_x       0.00741490  0.00002486  298.23 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8201 on 8351 degrees of freedom
## Multiple R-squared:  0.9142, Adjusted R-squared:  0.9142 
## F-statistic: 8.894e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_900, 
           coin_y = pricing_data_900[["USDT_REP"]], 
           coin_x = pricing_data_900[["USDT_BTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7288 -0.5774 -0.1290  0.4189  4.2573 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) -9.73062649  0.17668477  -55.07 <0.0000000000000002 ***
## coin_x       0.00740622  0.00004327  171.16 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8245 on 2783 degrees of freedom
## Multiple R-squared:  0.9132, Adjusted R-squared:  0.9132 
## F-statistic: 2.929e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_1800, 
           coin_y = pricing_data_1800[["USDT_REP"]], 
           coin_x = pricing_data_1800[["USDT_BTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7184 -0.5726 -0.1294  0.4224  4.2610 
## 
## Coefficients:
##                Estimate  Std. Error t value            Pr(>|t|)    
## (Intercept) -9.76197830  0.24983070  -39.07 <0.0000000000000002 ***
## coin_x       0.00741325  0.00006119  121.15 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8245 on 1391 degrees of freedom
## Multiple R-squared:  0.9134, Adjusted R-squared:  0.9134 
## F-statistic: 1.468e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_7200, 
           coin_y = pricing_data_7200[["USDT_REP"]], 
           coin_x = pricing_data_7200[["USDT_BTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5779 -0.6011 -0.1128  0.4236  2.6516 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -9.7521113  0.4882912  -19.97 <0.0000000000000002 ***
## coin_x       0.0074100  0.0001196   61.95 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8108 on 347 degrees of freedom
## Multiple R-squared:  0.9171, Adjusted R-squared:  0.9168 
## F-statistic:  3838 on 1 and 347 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_14400, 
           coin_y = pricing_data_14400[["USDT_REP"]], 
           coin_x = pricing_data_14400[["USDT_BTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.55987 -0.59252 -0.09366  0.44002  2.14749 
## 
## Coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) -9.6484195  0.6844643  -14.10 <0.0000000000000002 ***
## coin_x       0.0073797  0.0001676   44.03 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8098 on 173 degrees of freedom
## Multiple R-squared:  0.9181, Adjusted R-squared:  0.9176 
## F-statistic:  1939 on 1 and 173 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_86400, 
           coin_y = pricing_data_86400[["USDT_REP"]], 
           coin_x = pricing_data_86400[["USDT_BTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.4944 -0.3292 -0.1622  0.4061  1.5361 
## 
## Coefficients:
##               Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) -6.9069160  1.4791046   -4.67             0.000074 ***
## coin_x       0.0066972  0.0003638   18.41 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6775 on 27 degrees of freedom
## Multiple R-squared:  0.9262, Adjusted R-squared:  0.9235 
## F-statistic: 338.9 on 1 and 27 DF,  p-value: < 0.00000000000000022

10. USDT_XMR and USDT_LTC Coin Pair

An examination of USDT_XMR and USDT_LTC across time resolutions.

plot_coins(df = pricing_data_300, 
           coin_y = pricing_data_300[["USDT_XMR"]], 
           coin_x = pricing_data_300[["USDT_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.7857  -1.6548  -0.3121   1.0235  24.4679 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.96177    0.23045   156.1 <0.0000000000000002 ***
## coin_x       1.13133    0.00371   304.9 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.976 on 8351 degrees of freedom
## Multiple R-squared:  0.9176, Adjusted R-squared:  0.9176 
## F-statistic: 9.297e+04 on 1 and 8351 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_900, 
           coin_y = pricing_data_900[["USDT_XMR"]], 
           coin_x = pricing_data_900[["USDT_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.7046  -1.6898  -0.3227   1.0009  24.1214 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.967359   0.398511   90.25 <0.0000000000000002 ***
## coin_x       1.131332   0.006417  176.29 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.971 on 2783 degrees of freedom
## Multiple R-squared:  0.9178, Adjusted R-squared:  0.9178 
## F-statistic: 3.108e+04 on 1 and 2783 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_1800, 
           coin_y = pricing_data_1800[["USDT_XMR"]], 
           coin_x = pricing_data_1800[["USDT_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.6872  -1.6639  -0.3182   0.9912  24.1493 
## 
## Coefficients:
##              Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.992859   0.560945   64.17 <0.0000000000000002 ***
## coin_x       1.130652   0.009035  125.14 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.957 on 1391 degrees of freedom
## Multiple R-squared:  0.9184, Adjusted R-squared:  0.9184 
## F-statistic: 1.566e+04 on 1 and 1391 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_7200, 
           coin_y = pricing_data_7200[["USDT_XMR"]], 
           coin_x = pricing_data_7200[["USDT_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.6386  -1.6524  -0.2642   0.9648  19.3184 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.99738    1.08940   33.04 <0.0000000000000002 ***
## coin_x       1.12981    0.01756   64.34 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.855 on 347 degrees of freedom
## Multiple R-squared:  0.9227, Adjusted R-squared:  0.9224 
## F-statistic:  4140 on 1 and 347 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_14400, 
           coin_y = pricing_data_14400[["USDT_XMR"]], 
           coin_x = pricing_data_14400[["USDT_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.5723  -1.8244  -0.2084   0.9656  19.3276 
## 
## Coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept) 35.71162    1.51967   23.50 <0.0000000000000002 ***
## coin_x       1.13329    0.02451   46.24 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.818 on 173 degrees of freedom
## Multiple R-squared:  0.9251, Adjusted R-squared:  0.9247 
## F-statistic:  2138 on 1 and 173 DF,  p-value: < 0.00000000000000022

plot_coins(df = pricing_data_86400, 
           coin_y = pricing_data_86400[["USDT_XMR"]], 
           coin_x = pricing_data_86400[["USDT_LTC"]])
## 
## Call:
## lm(formula = coin_y ~ coin_x, data = df)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -5.410 -1.666  0.186  1.522  5.396 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept) 39.92702    2.45102   16.29  0.00000000000000172 ***
## coin_x       1.05803    0.04013   26.36 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.415 on 27 degrees of freedom
## Multiple R-squared:  0.9626, Adjusted R-squared:  0.9612 
## F-statistic: 695.1 on 1 and 27 DF,  p-value: < 0.00000000000000022